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Yes, theoretically it is possible to impact the Moon with enough moment and low enough energy to have it change its rotation periode, which actually is the same as its orbital periode (this is the tidal lock). Best candidate will be a high-mass, low-speed asteriod impacting almost tangentially and on the rotation plane.

Is this really possible? I would bet that it will never happen.

Supossing that it happens, will Moon get tidal locked again? Yes. As long as there are water on Earth suffering tides from Moon, these same water will attract one side of the Moon differentially from the other, so Moon will get locked again with the same face towards us.

It is a nice answer that you make here, but it would be particularly nice if it were a bit more quantitative. It would take just about one minute to figure out the mass the asteroid should have to unlock the moon, or the times over which the moon would get locked again, but the answer would have been so much more informative.
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Alexey BobrickJan 4 '14 at 12:48

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The other thing is that water isn't the only reason why tidal locking occurs. There can exist tides in the rocks on the planet or moon's surface (i.e. - mountains) which can cause this to happen. An example of this is the Pluto/Charon system, which are tidally locked to one another.
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astromaxJan 4 '14 at 16:48

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with the same face towards us -- that is surely wrong: which face the moon will show must be a random effect.
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WalterJan 6 '14 at 17:51

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Hi @Walter, but it is not. At least, not completely random, as the density is not the same on the "seas" face of the Moon and the other one.
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EnviteJan 6 '14 at 22:01

@Walter: It is an interesting question we are getting at here. One should compare the quadrupole moment of the Moon to that of the tidal buldge perhaps to get an idea of the answer.
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Alexey BobrickJan 7 '14 at 23:52